Average Error: 6.6 → 0.4
Time: 39.2s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot x \le -8.534245550996871115175132035540626568645 \cdot 10^{275}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \cdot x \le -3.472696779446323935386925227685759967005 \cdot 10^{-166}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \cdot x \le 2.024155232095970608846100533696018819805 \cdot 10^{-258}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \cdot x \le 2.475358399731635635401152366260838826524 \cdot 10^{251}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot x \le -8.534245550996871115175132035540626568645 \cdot 10^{275}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;y \cdot x \le -3.472696779446323935386925227685759967005 \cdot 10^{-166}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;y \cdot x \le 2.024155232095970608846100533696018819805 \cdot 10^{-258}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;y \cdot x \le 2.475358399731635635401152366260838826524 \cdot 10^{251}:\\
\;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\end{array}
double f(double x, double y, double z) {
        double r33359742 = x;
        double r33359743 = y;
        double r33359744 = r33359742 * r33359743;
        double r33359745 = z;
        double r33359746 = r33359744 / r33359745;
        return r33359746;
}
↓
double f(double x, double y, double z) {
        double r33359747 = y;
        double r33359748 = x;
        double r33359749 = r33359747 * r33359748;
        double r33359750 = -8.534245550996871e+275;
        bool r33359751 = r33359749 <= r33359750;
        double r33359752 = z;
        double r33359753 = r33359747 / r33359752;
        double r33359754 = r33359753 * r33359748;
        double r33359755 = -3.472696779446324e-166;
        bool r33359756 = r33359749 <= r33359755;
        double r33359757 = r33359749 / r33359752;
        double r33359758 = 2.0241552320959706e-258;
        bool r33359759 = r33359749 <= r33359758;
        double r33359760 = 2.4753583997316356e+251;
        bool r33359761 = r33359749 <= r33359760;
        double r33359762 = 1.0;
        double r33359763 = r33359762 / r33359752;
        double r33359764 = r33359749 * r33359763;
        double r33359765 = r33359752 / r33359747;
        double r33359766 = r33359748 / r33359765;
        double r33359767 = r33359761 ? r33359764 : r33359766;
        double r33359768 = r33359759 ? r33359754 : r33359767;
        double r33359769 = r33359756 ? r33359757 : r33359768;
        double r33359770 = r33359751 ? r33359754 : r33359769;
        return r33359770;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.6
Target6.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* x y) < -8.534245550996871e+275 or -3.472696779446324e-166 < (* x y) < 2.0241552320959706e-258

    1. Initial program 15.9

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity15.9

      \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac0.6

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{z}}\]

    5. Simplified0.6

      \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]

    if -8.534245550996871e+275 < (* x y) < -3.472696779446324e-166

    1. Initial program 0.3

      \[\frac{x \cdot y}{z}\]

    if 2.0241552320959706e-258 < (* x y) < 2.4753583997316356e+251

    1. Initial program 0.2

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied div-inv0.3

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]

    if 2.4753583997316356e+251 < (* x y)

    1. Initial program 40.7

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \le -8.534245550996871115175132035540626568645 \cdot 10^{275}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \cdot x \le -3.472696779446323935386925227685759967005 \cdot 10^{-166}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \cdot x \le 2.024155232095970608846100533696018819805 \cdot 10^{-258}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \cdot x \le 2.475358399731635635401152366260838826524 \cdot 10^{251}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))